Well-posedness for a multi-dimensional viscous liquid-gas two-phase flow model

TL;DR

This paper studies the mathematical well-posedness of a multi-dimensional viscous liquid-gas two-phase flow model, establishing conditions for existence, uniqueness, and continuation of solutions in various initial data settings.

Contribution

It proves global and local existence and uniqueness results for the model's solutions, including a continuation criterion, in the framework of Besov spaces.

Findings

Global existence and uniqueness near stable equilibrium

Local existence and uniqueness for general initial data

A continuation criterion for solutions

Abstract

The Cauchy problem of a multi-dimensional ($d\geqslant 2$) compressible viscous liquid-gas two-phase flow model is concerned in this paper. We investigate the global existence and uniqueness of the strong solution for the initial data close to a stable equilibrium and the local in time existence and uniqueness of the solution with general initial data in the framework of Besov spaces. A continuation criterion is also obtained for the local solution.